Noname manuscript No.(will be inserted by the editor)

A single-camera, 3D scanning velocimetry system for quantifying activeparticle aggregations

Matt K. Fu · Isabel A. Houghton · John O. Dabiri

Received: date / Accepted: date

Abstract A three-dimensional (3D) scanning velocimetry system is developed to quantify the 3D configu-rations of particles and their surrounding volumetric, three-component velocity fields. The approach uses atranslating laser sheet to rapidly scan through a volume of interest and sequentially illuminate slices of the flowcontaining both tracers seeded in the fluid and particles comprising the aggregation of interest. These imageslices are captured by a single high-speed camera, encoding information about the third spatial dimensionwithin the image time-series. Where previous implementations of scanning systems have been developed foreither volumetric flow quantification or 3D object reconstruction, we evaluate the feasibility of accomplishingthese tasks concurrently with a single-camera, which can streamline data collection and analysis. The capabilityof the system was characterized using a study of induced vertical migrations of millimeter-scale brine shrimp(Artemia salina). Identification and reconstruction of individual swimmer bodies and 3D trajectories withinthe migrating aggregation were achieved up to the maximum number density studied presently, 8 × 105 animalsper m3. This number density is comparable to the densities of previous depth-averaged 2D measurements ofsimilar migrations. Corresponding velocity measurements of the flow indicate that the technique is capable ofresolving the 3D velocity field in and around the swimming aggregation. At these animal number densities,instances of coherent flow induced by the migrations were observed. The accuracy of these flow measurementswas confirmed in separate studies of a free jet at ReD = 50.

Keywords First keyword · Second keyword · More

1 Introduction

Turbulent flows containing dispersed particles are a common feature in many environmental and industrialprocesses. The particles within these flows include both passive phases such as solid particles (Balachandarand Eaton, 2010), bubbles (Rensen et al., 2005; Risso, 2018), and droplets (Aliseda and Heindel, 2021), as wellas ‘active’ phases such as swimming zooplankton (Jumars et al., 2009). At sufficiently large particle volumefractions (10−6 ≤ Φv ≤ 10−3), the presence of the particles creates unique flow dynamics associated with the

Funding for this project was generously provided by the Gordon and Betty Moore Foundation

M. K. Fu and J. O. DabiriCalifornia Institute of TechnologyGALCIT1200 E California Blvd.MC 105-50Pasadena, CA 91125E-mail: mkfu@alumni.princeton.edu

I. A. HoughtonSofar OceanPier 50, Shed B, Bulkhead OfficeSan Francisco, CA 94158

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2 Matt K. Fu et al.

two-way fluid-particle coupling that are distinct from single-phase turbulence (Elghobashi, 1994). Characterizingthis two-way coupling requires accurately reconstructing the three-dimensional (3D) aggregations of particlesand the turbulent flow field in which they are dispersed. Because the fluid-particle interactions are 3D and occurover a wide range of spatiotemporal scales, there are many challenges to measuring them experimentally. Thesechallenges are exacerbated in denser aggregations where there are larger numbers of particles and interactionsthat need to be tracked and quantified (Bourgoin and Xu, 2014).

Biologically generated turbulence is an emerging topic whose study is currently limited by an inability toquantify the flow within aggregations of swimming plankton. The turbulence created by these aggregationsremains a poorly understood, and potentially underrepresented, source of scalar transport and ocean mixing(Kunze, 2019). Though the eddies created by an isolated swimmer are comparable to that of the individualorganism, the larger length scales associated with the aggregations of swimmers have the potential to introducemixing scales relevant to the surrounding water column. Recent laboratory studies of millimeter-scale brineshrimp (Artemia salina) aggregations using two-dimensional (2D) flow measurement techniques have shownthat induced migrations could generate aggregation-scale mixing eddies through a Kelvin-Helmholtz instabil-ity (Wilhelmus and Dabiri, 2014) with effective turbulent diffusivities several orders of magnitude larger thanmolecular diffusion alone (Houghton et al., 2018; Houghton and Dabiri, 2019). Though the potential for en-hanced mixing is substantial, direct measurements of enhanced turbulent dissipation and mixing in lakes andthe ocean due to vertical migrations have been less conclusive (Noss and Lorke, 2014; Simoncelli et al., 2018;Kunze, 2019). Parameterizing the precise conditions and mechanisms that lead to enhanced mixing remains anactive area of research (Wang and Ardekani, 2012, 2015; Ouillon et al., 2020; More and Ardekani, 2021).

There are numerous efforts to develop volumetric velocimetry techniques capable of resolving the unsteadyflow field in addition to the morphology and kinematics of a single swimming organism. A common techniquefor volumetric, three-component (3D-3C) velocity measurements is tomographic particle image velocimetry(Tomo-PIV), which has been used extensively for investigations of aquatic locomotion, including the propulsivemechanisms of fish (Gemmell et al., 2019) and pteropods (Adhikari et al., 2016). A key requirement for Tomo-PIV is employing four or more cameras to provide sufficient viewing angles for the tomographic reconstructionof both tracer particles used for flow quantification and swimmer bodies. Though there have been significantadvancements in the resolution of Tomo-PIV for velocity quantification, most notably, through the ‘Shake-the-Box algorithm’ of Schanz et al. (2016), accurately reconstructing active or passive particles with complex,three-dimensional shapes remains challenging. One common approach to body reconstruction is to compute avisual hull based on the projection of an object onto multiple camera viewpoints (Adhikari and Longmire, 2012).This method can overestimate the body size and obscure complex or rounded body geometries. While theseshortcomings can be moderated by prescribing additional constraints to the body morphology or kinematics,such an approach typically requires a priori knowledge of the behavior of the dispersed phase (Ullah et al.,2019). Despite these advancements, accurately reconstructing dense aggregations of particles, especially thosewith complex morphology, remains elusive.

Beyond Tomo-PIV, several alternative 3D-3C techniques have been proposed for marine swimming quantifi-cation, including plenoptic imaging (Tan et al., 2020), synthetic aperture particle image velocimetry (Mendelsonand Techet, 2015, 2018), defocusing digital particle image velocimetry (DDPIV) (Pereira and Gharib, 2002;Troutman and Dabiri, 2018), and 3D digital holography (Gemmell et al., 2013). Though all of these techniqueshave been demonstrated on individual swimmers, few are suitable for object reconstruction, and none havebeen successfully deployed to reconstruct dense configurations of swimmers and tracer particles in 3D.

Here, we present a 3D scanning system to reconstruct configurations of vertically migrating swimmers andquantify their surrounding 3D-3C velocity field. Several scanning systems have been developed in recent yearsfor a variety of applications, including 3D-3C velocity measurements (Hoyer et al., 2005; Brucker et al., 2013;Lawson and Dawson, 2014; Ni et al., 2015; Kozul et al., 2019) and 3D object reconstruction of translucentorganisms (Katija et al., 2017, 2020) and structures (Su et al., 2018). The 3D scanning system in the presentstudy is conceptually similar to those existing systems but is used to simultaneously quantify the locationsand organizations of the swimmers and their surrounding flow field. The approach relies on a laser sheet thatrapidly and repeatedly scans through a volume of interest, sequentially illuminating image slices of flow tracerparticles and organism cross-sections. The images are captured by a single high-speed camera, encoding detailedinformation about the third spatial dimension within the image time-series. Repeated scanning creates a seriesof image volumes consisting of swimmer bodies and tracer particles. Due to their large size relative to thetracer particles, the swimmer bodies can be identified and tracked over time. Similarly, the velocity field in thevicinity of the swimmers is determined via localized 3D cross-correlations of consecutive tracer particle images.

Scanning PIV System for quantifying migrating zooplankton aggregations 3

The capabilities of the technique are demonstrated by scanning induced vertical migrations of brine shrimp(Artemia salina). We demonstrate that the 3D position, orientation, and morphology of individual A. salinacan be faithfully reconstructed, even at large animal number densities up to 8×105 animals per m3, the high endof previously reported brine shrimp number densities in the literature (Houghton and Dabiri, 2019). We thenshow selected examples in which a coherent, large-scale induced flow is resolved by the measurement technique.While the appearance of large-scale induced flow was not observed during each migration, the present resultsdemonstrate the ability of the measurement technique to capture those dynamics when they do occur. Lastly,the outlook for the technique is discussed with suggested technical improvements to the system design.

2 Scanning 3D Image Reconstruction System

2.1 Imaging Hardware and Procedure

Fig. 1: Diagram of the scanning system. A mirror-mounted galvanometer (left) deflected the imaging laser alongthe scanning direction. A condenser lens (center-left) collected the angled beams to create displaced but parallelbeams. The beams were then formed into scanning sheets by a long sheet forming optic (center-right). Theimaging volume (right) was repeatedly scanned to sequentially illuminate slices of tracers and particles. Theimage slices were captured by a high-speed camera (lower-right) and then stacked to form 3D image volumes.

The design of the scanning system, shown in Figure 1, was similar to the system of Lawson and Dawson(2014). Illumination for the scanning was provided by a 671 nm continuous wave laser (5-Watt Laserglow LRS-0671 DPSS Laser System). This wavelength of light ensured that the brine shrimp exhibited no phototacticresponse to the imaging light. Additionally, the laser beam had only a single Transverse Electric Mode (i.e.,near TEM00 or quasi-Gaussian beam) to minimize imaging artifacts along the scanning dimension due to thebeam shape.

The laser beam was angled along the scanning dimension of the imaging volume by a mirror with a broad-band dielectric coating (-E02) mounted on a single-axis galvanometer (Thorlabs GVS211/M). The angularrange (max ±20◦) and bandwidth (65 Hz square wave at 50% full travel) of the galvanometer were comparableto other scanning systems in the literature that rely on scanning optics such as rotating polygonal mirrors(Hoyer et al., 2005; Brucker et al., 2013) or piezo-electric mirrors (Ni et al., 2015). An analog voltage signalfrom an arbitrary function generator (Tektronix AFG3011C) controlled the tilt of the mirror, which determinedthe position and scanning rate of the laser. The angled beams were collected by a 250 mm dia. condenser lens(370 mm back focal length), realigning them into parallel trajectories displaced along the scanning direction.These scanning beams were then converted into scanning sheets by a sheet forming optic that spans the depthof the imaging volume, such as a glass cylinder. The size of the condenser lens and the length of the sheet

4 Matt K. Fu et al.

forming optic determined the maximum distance over which the beams could be collected and aligned. Byemploying a condenser lens with a relatively large focal length, the amount of mirror rotation necessary todeflect the beams over the entire depth of field was contained to just a few degrees (±1.2◦ in the presentstudy). Here, the galvanometer was driven with a sawtooth wave to repeatedly scan the imaging volume witha constant forward scanning speed that filled approximately 94% of the scanning period. The remaining 6% ofthe scanning period was spent on the backward scan to reset the mirror position for the next imaging period.The accuracy of the scanning rate was limited by the repeatability of the galvanometer (0.07% for 30µradbeam angle repeatability).

By rapidly scanning a laser sheet along the sheet-normal axis, 1 millimeter-thick image slices throughoutthe depth of the interrogation volume were sequentially illuminated and captured by a high-speed camera. Byensuring that the scanning period was considerably faster than the flow time scales (e.g. laser translation speed30 times faster than the animal swimming speed in the present experiments), the recorded images could encodespatial information about the scanning dimension within the image time-series. The image sequences werestacked to construct volumetric (3D) images of the quasi-static tracers and larger active or passive particles,such as the swimmers of present interest. Periodic scanning of the interrogation volume facilitated tracking ofthe particles and tracers over time.

2.2 Imaging Acquisition & Calibration

The scanned images were captured with a high-speed camera (Photron FASTCAM SA-Z) equipped with afixed focal length macro lens (Micro-NIKKOR 105 mm with a 36 mm extension tube) at 1024 × 1024 px2

resolution. The image acquisition rate was matched to the scanning speed such that the displacement of thelaser sheet between each frame was approximately the same size as the mean pixel resolution (i.e., 40µm). Thisfine depth-wise sampling allowed the raw image volume to have a nearly isotropic voxel size. Both the f-number(f/22) and working distance (approximately 0.4 − 0.5m) were iteratively tuned to ensure that the entirety ofthe imaging volume was within the depth of field (3 cm) and each scanned image was in sharp focus.

A custom 3D calibration target (UCrystal) was fabricated to calibrate the imaging volume and accountfor the 7% change in magnification along the scanning depth. The target, shown in Figure 2a, comprised an8 cm × 8 cm × 8 cm crystal cube internally laser engraved with a 3-dimensional grid of 1.6 mm diameterspherical shells. The shells were evenly spaced 1 cm apart in each direction to form a 6 × 6 × 6 cubic array(5 cm × 5 cm ×5 cm), which was centered within the crystal. The spot size of the laser engraver used to rasterthe spherical shells was approximately 100 µm. The cube was suspended at the center of the imaging volumeand aligned with the imaging coordinate system to ensure that the laser sheet was not deflected by refractioninside the cube.

Calibrating the imaging system involved scanning the calibration cube with the laser sheet and capturingthe 2-D image slices with the high-speed camera. The images collected over each period were stacked to forma single 3-D image volume. Because the scanning was designed to create nearly isotropic volumes, minimalprocessing of out-of-plane dimension was necessary to render scanned objects.

The raw image volumes were processed and analyzed using MATLAB’s Image Processing Toolbox to recon-struct and locate the spherical targets. The image volume was median filtered (73 vx. stencil) and binarized witha global threshold based on the image histogram. Morphological area opening was then used to remove objectsother than the calibration spheres, e.g., tracer particles and camera noise, from the binary image, leaving justthe calibration spheres. Any holes within the binary images of the spheres were then filled. The centroids of theremaining spheres (shown in Figure 2b) were then used to calibrate the image volume. While all of the targetspheres were scanned, not all of them were successfully reconstructed. This failure was most common in targetspheres further from the camera as their scattered light could be obstructed by spheres in the foreground.

By relating the centroids of the rendered spheres to the known dimensions of the calibration target, thevoxels within the image volume could be mapped to 3D coordinates in physical space. The mapping betweenthe two coordinate systems was calculated using the MATLAB estimateCameraParameters function.

2.3 Particle Segmentation

Just as the spheres were extracted from the calibration target, we do the same for the active/passive particlesin an aggregation. Because the particles in this study, i.e., the swimmers, were significantly larger than thetracers, they could be identified and segmented within the image volume by size. This segmentation process was

Scanning PIV System for quantifying migrating zooplankton aggregations 5

(a) (b)

Fig. 2: Images of the calibration cube target. (a) CAD Rendering of the 3D calibration cube. The 6 × 6 × 6array of spheres can be seen in the center of the 8× 8× 8 cm3 cube. (b) Rendered scan of the calibration cubefrom the 3D scanning system. Some spheres are not reconstructed in the image due to low scattering intensity.

accomplished by filtering the raw images with a cubic Gaussian kernel (3 vx. stencil). The filtered images werethen binarized with the method of Otsu (Otsu, 1979), which computes a global threshold based on the imagehistogram. Tracers were removed from the binary image by filtering out objects smaller than 8000 connectedvoxels through morphological area opening. This 8000-voxel threshold was found to work satisfactorily for thespecific imaging parameters in this study. Depending on the application and object size distribution, alternativesegmentation techniques, such as the 3D analogs of those reviewed by Khalitov and Longmire (2002), may provemore robust. Connected components within the binary image were labeled as individual swimmer bodies. Thecentroids of each of the swimmer bodies were tracked over time to determine the swimmer trajectories. A maskfor the tracer field was computed by morphologically dilating the binary image of the particles with a sphericalstructuring element (4 vx. radius).

2.4 Velocity Field Registration

With the particles comprising the aggregation segmented, the remainder of the image corresponding to thetracer field was then used to compute the volumetric, three-component velocity field by registering the localdisplacements of tracer particles between successive images. Each pair of image volumes was first masked usingthe binary images of swimmer bodies from the previous segmentation step. Each mask was applied to bothimages in the pair to ensure each frame had an identical mask and avoid correlations due to mask shifting.

To resolve the local tracer displacement between consecutive images, we employed a modified version ofthe Fast Iterative Digital Volume Correlation (FIDVC) Algorithm of Bar-Kochba et al. (2015). This methodcould resolve large volumetric deformations between two images by conducting 3D cross - correlations onprogressively refined interrogation windows to compute the local image displacement. First, the original imageswere divided into 64 × 64 × 64 vx3 windows with 50% overlap. Each windowed image was weighted with themodular transfer function of Nogueira et al. (2005) to stabilize the spatial frequency content. The 3D, voxeldisplacement between the two images was determined to the nearest integer voxel by finding the local maximumof the cross-correlation function between the two windows. Sub-voxel resolution for the displacement was thenachieved by first conducting a least-squares fit with a 3D Gaussian function to the 53 voxel neighborhoodaround the peak value in the cross-correlation function. The sub-voxel displacement was then determined bysolving for the local maximum of the resulting fit.

Displacement vectors with correlation coefficients below a certain threshold (≤ 0.01% of the maximumcorrelation) or within the image mask were rejected and replaced with interpolated values. The displacementfield was then filtered with the tunable low pass convolution filter of Schrijer and Scarano (2008) to improve the

6 Matt K. Fu et al.

iterative image deformation, and all nonphysical outliers were removed via a universal median test (Westerweeland Scarano, 2005). Both image volumes were then symmetrically deformed by a tri-cubic interpolation schemeusing the MATLAB griddedInterpolant function. The root mean square (RMS) deviations between the twoimages before and after deformation were computed and their ratio was used as a convergence metric. Whenthe RMS deviation ratio was reduced to less than 0.1, the window size was refined for the next iteration.The iterative deformation process was repeated until the minimum window size (32 × 32 × 32 vx3 with 75%overlap) was reached and the final RMS ratio was less than 0.2. These convergence criteria were found toprovide an acceptable balance between accuracy and computation times for the images analyzed in this studyand typically required 7 iterations to achieve convergence. All Fast Fourier Transforms (FFTs) and sub-voxelestimation operations were executed with the MATLAB Parallel Computing Toolbox on two NVIDIA QuadroRTX5000 GPUs with double precision. This GPU variant was benchmarked against the original FIDVC code(Bar-Kochba et al., 2015) with agreement found in all cases up to single precision.

3 Induced Vertical Migrations of Artermia Salina

(a) (b) (c)

Fig. 3: Illustration of the Artemia salina vertical migration and image acquisition. (a) The brine shrimp werecollected at the bottom of the 1.2 m tall tank with an upward projecting LED light stimulus (PeakPlus LFX1000,600 lumens). After the Artemia salina reached the bottom, the tank was allowed to settle for at least 20 min. toensure the fluid was quiescent. (b) An upward migration was induced with a similar downward projecting lightstimulus at the top of the tank. An additional light was used to steer the brine shrimp horizontally along thefree surface to the side of the tank, reducing the number of swimmers that would accumulate and obstruct thedownward projecting light. The imaging volume was positioned along the central axis of the tank approximately40 cm below the tank free surface. (c) A downward migration was induced with the first upward-facing lightto return the shrimp to the bottom of the tank.

To test the capability of the technique in capturing aggregation kinematics and associated fluid mechanics,we evaluated vertical migrations of brine shrimp (Artemia salina) within a laboratory tank following themethodology of Houghton et al. (2018) and Houghton and Dabiri (2019) and imaged the resulting flow. Thisapplication was selected due to the challenge that the animal number density presented to existing techniques.Additionally, the slow evolution of the migration was compatible with the achievable scanning rate of thecurrent system (O(1) sec). By leveraging the positive phototaxis of A. salina towards sources of blue and green

Scanning PIV System for quantifying migrating zooplankton aggregations 7

wavelengths of light, coordinated swimming of a brine shrimp aggregation could be directed up and down theheight of a 1.2-meter tall vertical tank (see Figure 3). A collection of approximately 40,000 ± 5, 000 animals(Northeast Brine Shrimp) was introduced to the tank for testing, corresponding to a tank-averaged abundanceof 130, 000 ± 16, 000 animals per m3. The brine shrimp had a typical body length of 5 mm and a nominalswimming speed of 5 mm/s. The tank was seeded with 13 µm CONDUCT-O-FIL silver coated glass spheres(Potters Industries, Inc.) to facilitate imaging of the flow field.

Before the migration, the animals were collected at the bottom of the tank using an upward facing lightstimulus (PeakPlus LFX1000, 600 lumens) introduced through the transparent floor of the water tank. Afterthe animals reach the bottom of the tank, the water was allowed to equilibrate for at least 20 minutes to ensurethe fluid was quiescent. Due to the slight negative buoyancy of A. salina, the animals were minimally activeat the bottom of the tank. To trigger the upward migration, the light stimulus at the bottom of the tankwas deactivated, and corresponding light stimuli at the top of the tank were activated. The first of these lights(PeakPlus LFX1000, 600 lumens) was directed down along the tank’s central axis in a 5±2 cm diameter columnand served as the primary stimulus to draw the animals up towards the free surface. A second horizontal light(PeakPlus LFX1000, 600 lumens), located just below the free-surface, steered the animals along the free surfaceand away from the primary stimulus to prevent them from accumulating and obstructing the migration. Theduration of the vertical migration, typically 5-6 minutes, extended from the triggering of the lights until theaccumulated A. salina began to obstruct the primary stimulus.

The 3D scanning system imaged the swimmer aggregation and tracers within in a 41×41×30 mm3 volumeapproximately 40 cm below the free surface. Throughout the vertical migration, scanning sequences were trig-gered at approximately 1-minute intervals to record a sequence of approximately 22,000 images, correspondingto a minimum of 26 image volumes over a 5 second period. The duration of the scanning sequence was limitedby the size of the camera internal buffer (32 GB), and the 1-minute interval between scanning events wasdictated by the time necessary to fully transfer the images to an external hard drive. Following the migration,the animals were returned to the bottom of the tank using the light stimulus under the transparent floor of thewater tank. The complete imaging volume specifications and scanning parameters can be found in Table 1.

Parameter Symbol Value

ScanningPara

meters

Field of View Lx×Ly 41 × 41mm2

Depth of Field Lz 30mm

Approx. Voxel Size 40 × 40 × 40µm3

Image Acq. Rate fc 4, 000 fps

Scanning Freq. fs 5 Hz

Scanning Speed us 15 cm · s−1

Sheet thickness h 1 mm

Sheet separation ∆z 40µm

Est. Seeding Density NV 1.7 × 10−4 ppv

No. Vols. per scan 26

Sheet step size ∆z 40µm

Shrimp Body Length `c 5 − 10mm

Rel. Swimming Speed Uswim 3 ± 1 mm/s

Tank-Avg. No. Density n 1.3 ± 0.16 × 105 m−3

No. laser sheets N 750

Non-dim Scan Speed us/Uswim 30

Non-dim Sheet Width h/∆z 20

Table 1: Imaging parameters for brine shrimp migrations

4 Results

4.1 Body Reconstruction and Tracking

Following the procedure outlined in section 2.3, individual shrimp bodies were segmented in the image volumeto directly assess their number, location, and orientation. A representative portion of a raw image volume isshown in Figure 4 from the camera viewpoint. Due to the translucent nature of the shrimp bodies, light was

8 Matt K. Fu et al.

Fig. 4: Typical subsection of raw image volume of vertical migration from the camera perspective. Imageintensity is inverted and colored for clarity. The shadowing effect from a foreground shrimp is outlined in blue.Reconstructed shrimp are shown in copper and outlined in red. Images of tracer particles can be seen as thedots interspersed throughout the image.

readily scattered off the organisms, allowing them to be identified as large coherent objects within the 3D imageamongst a field of smaller tracer particles. An example of two imaged shrimp are visible in the left side of Figure4 with a copper coloring and outlined in red for clarity. While most of the details of the shrimp morphologyare evident in the image, fine features such as the shrimp legs and tail are attenuated and blurred. Due tothe nature of single-camera imaging, details of the shrimp bodies and particles can be obscured or altogetherblocked by objects in the foreground. An example of this shadowing effect is shown outlined in blue on the rightside of Figure 4. Both the lack of visible particles and resemblance of the shadowed area to a shrimp silhouetteindicated the presence of a shrimp located between the imaging volume and the camera.

The ability of the technique to reconstruct configurations of brine shrimp during a vertical migration isillustrated in Figure 5, which shows a scanned reconstruction of the animals within the full imaging volume.The approximately 40 shrimp bodies are reproduced from a scan conducted approximately four minutes intothe migration and represent one of the densest collections of animals imaged during the measurement campaign.Figure 5a shows all of the reconstructed shrimp visualized within the imaging volume. The shrimp coloringindicates their depth-wise location with positive values corresponding to locations closer to the camera. Thesesegmented images have been corrected to account for the camera perspective and deblurred along the scan-ning dimension to compensate for the finite sheet thickness using Richardson–Lucy deconvolution (Biggs andAndrews, 1997). Despite the deblurring process, some elongation of the bodies in the scanning dimension wasstill evident. Figures 5b-5d show renderings of one animal in the migration from different viewing angles. Thiselongation from the scanning was most apparent in the animals tails, which appeared thicker along the scanningdimension than in the imaging plane. In the future, this effect could be mitigated through further narrowing ofthe laser sheet with additional optical components. Similarly, these figures also illustrate the effect of the cameraperspective on the reconstruction quality. Body morphology within the line-of-sight of the camera (seen fromFigure 5c) was reconstructed with higher fidelity than those obscured by the shrimp body. These differencesare apparent in Figures 5b and 5d where details such as the organisms legs were reconstructed on the right sideof the organism (large values of z) but were absent from the left side of the organism (smaller values of z).

Even with these limitations, the reconstructed swimmers were able to capture the 3D locations, bodymorphology, and orientations of the scanned organisms. Though alternative single-camera techniques, such asDDPIV (Troutman and Dabiri, 2018), can similarly track particle locations in 3D, extracting a comparablelevel of body-specific information is neither straightforward for isolated swimmers nor possible at the highnumber densities present in these aggregations. Furthermore, the average animal number density measured inthis scan, 8 × 105 animals per m3, was at the upper bound of animal number density estimates conducted inprevious laboratory experiments (Houghton et al., 2018; Houghton and Dabiri, 2019). Where previous studieshad to infer the animal number density during migration from depth-averaged 2D measurements, the currentsystem was capable of measuring this quantity directly.

With the individual organisms identified, we tabulated the number of shrimp in each frame to observethe spatial and temporal evolution of the animal number density. A plot of the average number density inthe imaging volume throughout four different migrations is shown in Figure 6. Reconstructions from Figure 5correspond to the fourth minute of the first migration. Unlike previous experiments, specifically Houghton and

Scanning PIV System for quantifying migrating zooplankton aggregations 9

(a)

(b) (c)

(d) (e)

Fig. 5: Reconstructed swimmer bodies from an induced vertical migration. (8 × 105 animals per m3).(a) Re-construction of animals within the full imaging volume. The direction of the migration was in the positivey-direction. The number of swimmers and their 3D locations and orientations could be reconstructed with thescanning technique. (b)-(d) Images of a single reconstructed swimmer from the migration shown from differentviewing angles. The 3D morphology of the swimmer was evident in the reconstruction, although some featuresof the shrimp were elongated along the scanning dimension. (e) A reference picture of Artemia salina.

0 2 4 60

2

4

6

8

·105

Time (min)

Avg.

No.

Den

sity

(an

imals

per

m3)

Mig. 1

Mig. 2

Mig. 3

Mig. 4

Fig. 6: Plot of the mean animal number density in the imaging volume over the duration of four induced verticalmigrations. The upper-most point corresponds to the visualization shown in Figure 5.

Dabiri (2019), where a steady-state saturation in the number of shrimp was observed after one to two minutes,we observed a slow but continual growth in the number of shrimp in the frame, even up to four minutes. Thisslower migratory behavior may be attributed to differences in the age and health condition of the organismstested presently or due to natural biological variability in the migratory behavior. For the present purposes, itis sufficient to note that the repeated measurements are qualitatively consistent.

10 Matt K. Fu et al.

Fig. 7: Plot animal trajectories from Figure 5 over the 5 sec. duration of the scan indicated by the color changefrom copper to black.

Figure 7 shows the animal pathlines over the scanning period associated with the swimmers reconstructedin Figure 5. For the scanning frequency used here (fs = 5 Hz), the displacement of individual shrimp betweenframes is typically a fraction of a body length. Because the displacement of each organism between frames issmall relative to the inter-organism spacing, we can successfully track most organisms in these experimentswith a nearest-neighbor search. More sophisticated particle tracking algorithms such as that of Ouellette et al.(2006) could improve the trajectory length and prediction.

4.2 Velocity Measurements

Corresponding contours of vertical velocity associated with the upward migration are shown in Figure 8. Figure8a shows contours of the vertical velocity contours taken from a scan taken approximately 2 minutes into themigration. This scan was obtained closer to the beginning of the migration and contained fewer animals withinthe imaging volume than Figure 5a. Consequently, the technique was able to resolve downward projectingwakes from the individual swimmers. Figure 8b shows contours of the vertical velocity associated with the scanshown in Figure 5a where the downward velocity was largest. A coherent downward motion of fluid throughthe aggregation was evident. This behavior was consistent with the observations of Houghton et al. (2018), whoqualitatively visualized a similar coherent downward flow from vertical migration A. salina using planar laser-induced fluorescence. These measurements indicate that the technique was capable of quantitatively resolvingthe 3D velocity field in and around the swimming aggregation.

5 Velocity Measurement Validation

Due to the lack of a ground truth reference to validate the velocity measurements in the vertical migrations,this capability of the measurement system was assessed by using a controlled laminar jet flow. By evaluatingthe system against a laminar jet flow without an aggregation present, we were able to ensure that it couldaccurately resolve the three-component, three-dimensional velocity field. Imaging was conducted in a small40 × 40 × 40 cm3 glass tank seeded with 100µm silver-coated glass spheres. A syringe pump provided a bulkflow of 21.50 mL/min into a length of Tygon tubing with an elliptical cross section (equivalent diameter,De = 8.7 mm) which exited as a laminar free jet flow of ReD = UbDe/ν, where Ub was the bulk jet velocity,and ν was the water kinematic viscosity (0.95 cSt at 22◦ C). The finite eccentricity of the cross-section wasdue to plastic deformation of the tube wall prior to installation. Illumination was provided by a 532 nm laserwith Gaussian beam shape. Here, the scanning speed, us, was 100 times larger than the jet’s bulk velocity,

Scanning PIV System for quantifying migrating zooplankton aggregations 11

(a)

(b)

Fig. 8: Vertical velocity contours from snapshots taken during a single migration. Swimmer masks within thePIV field are shown in tan. Blue and red isosurfaces denote contours of negative and positive vertical velocity,respectfully. (a) Vertical velocity field 2 minutes into the migration. Downward velocity (blue) associated withthe wakes of the swimming was resolved. (b) Vertical velocity field 4 minutes into the migration. Downwardvelocity (blue) contours associated with Figure 5a. Instead of individual wakes, a coherent downward motionwas present through the migration.

which was sufficient to resolve the 3D particle positions with minimal error related to the finite scanning speed(Kozul et al., 2019). Imaging parameters and jet specifications are listen in Table 2.

Measurements of the out-of-plane velocity component aligned with the scanning direction were verified byscanning the jet in two different orientations, as shown in Figure 9. In the first orientation (given by the bluejet in Figure 9a), the axis of the jet was parallel to the scanning direction such that the jet flow was normal tothe imaging plane. An image slice of the jet in this configuration can be seen in Figure 9b with the ellipticalcross-section of the wall illuminated by the imaging sheet. Correspondingly, the tracer particle motion wasprimarily out of the page. In the second orientation (given by the green jet in Figure 9a), the jet’s axis wasperpendicular to the scanning direction, and the tracer particle displacements were primarily contained withinthe same imaging plane. In the corresponding image slice (see Figure 9c), the imaged cross-section of the tubeinstead appeared rectangular, and the fluid advection was from left to right. Resolving the flow in the first

12 Matt K. Fu et al.

Fig. 9: Diagrams of the scanning system setup for flow velocity measurement validation. (a) Top view of theexperimental setup. From this viewpoint, the scanning direction was parallel with the page’s height, and theimaging planes were aligned with the page width and normal directions. The two orientations of the jet flowmeasured in this experiment corresponding to flow normal and parallel to the imaging plane are blue andgreen, respectively. (b) Image of tracer field and jet outlet in the out-of-plane orientation. The optical axisof the camera was parallel to the axis of the jet, and flow was out of the page. The elliptical cross-sectionseen in the image was due to plastic deformation of the tube prior to installation and was present in bothconfigurations. (c) Image of tracer field and jet outlet as imaged from the in-plane orientation. The optical axisof the camera was perpendicular to the axis of the jet, and the flow advection was from left to right.

configuration depended on the ability of the technique to reconstruct tracer particle location along the scanningdimension. There, the velocity calculations correlated particles across different image sheets. Conversely, in thesecond configuration, velocity calculations were far less sensitive to the scanning effect as fluid motion wasprimarily contained within the image plane. Consequently, the fluid motion could still be determined withoutexplicitly relying on the particles motions in adjacent image sheets similar to conventional 2D PIV. Hence, thein-plane jet measurement provided a ground truth reference for the out-of-plane measurements.

Parameter Symbol Value

ScanningPara

meters Field of View Lx×Ly 100 × 100mm2

Depth of Field Lz 47mm

Approx. Voxel Size 100 × 100 × 100µm3

Image Acq. Rate fc 5,000 fps

Scanning Freq. fs 10 Hz

Scanning Speed us 50 cm · s−1

e−2 Sheet thickness h ≈ 1 mm

Sheet step size ∆z 100µm

Jet

Bulk Velocity Ub 5.4 ± 0.1mm/s

Equivalent Diameter De 8.7 ± 0.2mm

Aspect Ratio 1.31

Reynolds Number ReD 50

Non-dim Sheet Speed us/Ub 92

Non-dim Sheet Width h/∆z 10

No. laser sheets N 475

No. of scans 40

Table 2: Imaging parameters for jet measurements

The two different configurations were evaluated by reorienting the jet within the tank while keeping theimaging system fixed. To evaluate the technique, we compared the maximum fluid velocities from each configu-

Scanning PIV System for quantifying migrating zooplankton aggregations 13

−1 0 1 2 3 4 5 60

1

2

X/D

|U| m

ax/Ub

Fig. 10: Maximum fluid velocity (Umax) exiting the round jet as a function of distance from the jet exit. Thegray area denotes measurements obtained inside the jet tube. ( ): Out-of-plane jet (blue) where the fluidvelocity was normal to the imaging plane. ( ): In-plane jet (green) where the velocity was parallel to theimaging plane. Blue and green bands correspond to the standard deviation of the local velocity measurementsin the out-of-plane and in-plane configurations, respectively.

0.51 2 3 4 5 6 7 8 9 100

2

4

6

8

10

Sheet Overlap (h/∆z)

%E

rror

inUm

ax

Fig. 11: Error in the max jet velocity calculation relative to h/∆z = 10 as a function of sheet overlap.

ration as a function of distance from the jet exit, as shown in Figure 10. Because the jet tube is translucent, thetechnique is capable of measuring velocity inside the jet tube (shaded in gray), albeit with a slight differencebetween the two orientations. In this region, the out-of-plane orientation measures approximately 5% largerthan its in-plane counterpart. Immediately outside the jet exit, there is excellent agreement between the twomeasurements over the extent of the domain. The distance over which data is reported for the out-of-planejet is considerably shorter than the in-plane jet due to the depth of field being smaller than the image width.Importantly, this test indicates that the setup is capable of resolving velocities both parallel and normal tothe imaging plane and is consistent with previously reported validations of scanning PIV (Brucker et al., 2013;Kozul et al., 2019).

Here, because of the fine sampling of the imaging volume, we were able to examine how the quality of thevelocity calculations along the optical axis degraded with increased sheet spacing. For the experiment conductedhere, the step size between consecutive images was approximately the voxel size which corresponded to a 90%overlap between adjacent sheets (i.e., h/∆z = 10). Here, we artificially increased the step size of our data setby first down-sampling the image volumes from full-resolution scans and then re-interpolating via tri-splinethe new images back to the full resolution. The images were then processed with the same cross - correlationalgorithm and compared with the full-resolution result (h/∆z = 10). Figure 11 shows how the mean differencebetween the max velocity calculation shown in Figure 10 varied as the effective step size between laser sheetswas increased. Importantly, even when the data was down-sampled by a factor of 2 (h/∆z = 5), there was anegligible change in the measured maximum jet velocity over the domain. Even downsampling the data by afactor of 3 (h/∆z = 3.33), yielded a mean error of approximately 2% over the imaging domain compared to thefull resolution measurement. Above this range, the error began to increase sharply as the spacing approachedthe sheet width. These empirical results were consistent with previous findings from comparable numericalinvestigations including Kozul et al. (2019) who found a sheet overlap of h/∆z = 5 to be sufficiently resolved

14 Matt K. Fu et al.

for particle tracking and Lawson and Dawson (2014) who found h/∆z = 3− 4 to be optimal for single camerameasurements.

6 Discussion and Conclusions

A 3D scanning velocimetry system for 3D-3C velocity measurements and particle aggregation reconstructionwas demonstrated using an induced vertical migration of A. salina. The technique successfully reconstructedthe swimmer bodies and their 3D configurations at animal number densities at the upper bound of those foundin previous laboratory migration experiments (8× 105 animal per m3), a task that had not been accomplishedwith previous methods. This capability will allow for more direct studies of the flow-structure interactionsthat enable individual animal wakes to coalesce into larger-scale flows. The success of this technique at theseanimal number densities suggest that it could have broader applications in the study of flows with dispersedparticles. The animal volume fractions measured in this study, Φv ≤ 1.7 ± 0.24 × 10−3, encompass the rangeof volume fractions (10−6 ≤ Φv ≤ 10−3) over which two-way coupling is exhibited between turbulence anddispersed particles (Elghobashi, 1994). This capability suggests that scanning techniques could be a robust toolfor studying this coupling in turbulent flows with translucent or transparent particles, such as bubbles anddroplets.

The most notable challenges for this system included the trade-offs between the temporal resolution of theflow field, illumination of the images, and the resolvable depth of field. The achievable depth of field in thepresent design was primarily constrained by the power of the laser. Increasing the depth of field to keep allof the scans in sharp focus required significantly reducing the image illumination due to compounding effectsof shrinking the lens aperture and increasing the camera frame rate. In the case of the former, reducing theaperture caused a quadratic reduction in the light intensity for a linear increase in the depth of field.

Future implementations of this technique can employ a telecentric lens on the high-speed camera to ensurea constant magnification throughout the entire image volume, eliminating any parallax. Additionally, this lenstype will also allow for a larger usable depth of field for a given aperture due to the symmetric image blurring.Similarly, incorporating a scanning lens into the setup could significantly improve the temporal capabilities ofthe scanning system. A scanning lens would allow the location of the focal plane to be adjusted over distancescomparable to the field of view at bandwidths exceeding the scanning frequencies. By synchronizing the focaldistance to the laser sheet location, the depth of field can be reduced to the thickness of the laser sheet andindividual images can be captured by the high-speed camera using a much larger aperture. This modificationwould allow for significantly greater illumination of the camera sensor than the current implementation wherethe focal plane is static, and the entire scanning distance must be contained within depth of field.

Lastly, because the technique relies on a single high-speed camera, it is compatible with many existing under-water imaging systems such as the diver operated self-contained underwater velocimetry apparatus (SCUVA)(Katija and Dabiri, 2008) or remotely operated DeepPIV (Katija et al., 2020, 2017). Adapting this techniquefor field deployment could enable 3D-3C velocity measurements of various environmental and biological flowsthat have traditionally been limited to 2D observations. Similar to the A. salina, there are numerous marineorganism whose feeding and swimming are potentially observable with this technique, including salps, jellyfish,siphonophores, and ctenophores. The ability to image the 3D flow in and around these organisms could providenumerous biological and fluid mechanical insights.

Acknowledgements The authors would like to thank Prof. Christian Franck for supplying the basis for the cross-correlationalgorithm used in this study. This work was supported by the U.S. National Science Foundation Grant, under Award Number1510607 and the Gordon and Betty Moore Foundation.

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